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Will_Sawin comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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You can search for reasons to cooperate in a much stronger formal system than you search for reasons to defect in. Is there any decision-theoretic justification for this?
If you do that, you're back in the same situation that you started with and are cooperating with CooperateBot again.
This is clearly not true for proposal 2. No matter the formal system, you will find a proof (YouDefect => OpponentCooperate), and therefore defect.